In plain words
The whole essence of all the texts of Vedānta I shall tell at once, in a single sentence: the Ātma that is in all living beings and I are one; hold this in your mind.
Embodiments of the divine Ātma!
The Veda is the whole body of true words revealed by the great ṛṣis who were seers of the mantras. The Veda is that which revealed the Satya that does not change, in the past, the future and the present. It is the Veda that gives welfare and security to the three worlds and establishes in society the Vijñāna it needs, and Śānti. The Veda is the in-breath and out-breath of the Supreme Person. It arose from the root vit. Vit means Jñāna. The Veda is that which is full of Jñāna. The Veda is infinite: ananto vai vedāḥ, it is said. Jñāna, too, is infinite.
For ordinary people to study this infinite Veda and master it fully is a very hard thing. To study so vast a Veda takes a great deal of time as well. So the ordinary man does not take up the study of the Veda at all. The great ṛṣi Vyāsa, seeing this truth, divided the Veda into four parts: he set apart all the ṛks and named them the Ṛk Saṃhitā. From this infinite Veda he set apart the whole of the Yajus and named it the Yaju Saṃhitā. He set apart the whole of the Sāma and named it the Sāma Saṃhitā. He set apart the Atharvaṇa mantras and named them the Atharvaṇa Veda. But it was to spread the principle that is the root and support of all of them through the world, to proclaim it, that he went on dividing it in this way, in many ways.
Each Saṃhitā he went on dividing into three parts: the Brāhmaṇa, the Āraṇyakas and the Upaniṣads. As for these Brāhmaṇas: he gave the world the forms and the nature of the mantras, and went on setting out the mantras fit for the yajñas, yāgas and other rites that are in them. Among these he divided the Brāhmaṇas four ways: the Vitareya Brāhmaṇa, the Kauśītaki Brāhmaṇa, the Śatapatha Brāhmaṇa and the Gopatha Brāhmaṇa. These are only the forms of the mantras chanted in yajñas, yāgas and other rites.